Hey, I’ve got a sudden question for you.
Probability distribution on a set of binary variables is to a quantum state
as ??? is to a unitary linear operator.
What should ??? be replaced with?
Here’s why I have this question. Somehow I was thinking about Normalizing flows, which are invertible functions which, when applied to a sample from an N-dimensional probability distribution, transform it into a sample from another N-dimensional probability distribution. And then I thought: isn’t this similar to how quantum operator is always unitary? Maybe then I can combine encoding an image as a pure state (like in Stoudenmire 2016 - Supervised learning with quantum-inspired tensor networks with representing quantum operators as tensor networks to get a quantum-inspired generative model similar to normalizing flows.
Any unitary linear operator (to make sure squared amplitudes still sum to 1). To your second question, I’ll post a toplevel comment.
Hey, I’ve got a sudden question for you. Probability distribution on a set of binary variables is to a quantum state as ??? is to a unitary linear operator.
What should ??? be replaced with?
Here’s why I have this question. Somehow I was thinking about Normalizing flows, which are invertible functions which, when applied to a sample from an N-dimensional probability distribution, transform it into a sample from another N-dimensional probability distribution. And then I thought: isn’t this similar to how quantum operator is always unitary? Maybe then I can combine encoding an image as a pure state (like in Stoudenmire 2016 - Supervised learning with quantum-inspired tensor networks with representing quantum operators as tensor networks to get a quantum-inspired generative model similar to normalizing flows.
Maybe stochastic matrix?